## aceace Group Title Logaritm Question!!! one year ago one year ago

1. aceace Group Title

Find a relation between x and y that does NOT involve logarithms: log x + log y = log (x+ y)

2. zepdrix Group Title

Can we assume it's a log of base 10?

3. aceace Group Title

yes i think so

4. AERONIK Group Title

logx + log y is never log(x+y) it seems... it is log(xy)

5. aceace Group Title

6. zepdrix Group Title

I suppose we could exponentiate both sides.. $\huge 10^{(\log x + \log y)}=10^{\log(x+y)}$ Using rules of exponents we can split up the left side like this: $\huge 10^{\log x}*10^{\log y}=10^{\log(x+y)}$ Recognizing that log base 10, and the exponentiation base 10 are inverse operations of one another, they essentially "cancel out". Giving us: $\huge xy=(x+y)$ $\huge y=\frac{x}{x-1}$

7. zepdrix Group Title

Something like that maybe? :o

8. geoffb Group Title

@zepdrix Oooh, sexy!

9. zepdrix Group Title

lol :3

10. aceace Group Title

@zeptr yes thats the answer !!!

11. zepdrix Group Title

Oh cool. :)

12. zepdrix Group Title

Were you just testing us or something? :D lol Knew the answer the whole time huh? XD

13. zepdrix Group Title

@AERONIK , it seems that logx+logy=log(x+y) sometimes. I wouldn't say NEVER. Obviously it doesn't match the rule for logs that we had in mind. But if you plug in y=2, x=2 into the original equation, that should work out ok as one solution :D Since 2+2 is the same as 2*2

14. aceace Group Title

no i had the answers at the back of book but i have no idea how to do it... i still dont get the logic though...

15. AERONIK Group Title

so it is not an identity and just a function you say ?

16. aceace Group Title

yeh just a random equation

17. zepdrix Group Title

Yah it appears it wasn't testing you on whether or not you knew your log identities, they just wanted to see a relationship between x and y. Interesting problem :O

18. AERONIK Group Title

and one more thing in your proof you have assumed the given statement to be correct, can you please give a formal proof for te same?

19. zepdrix Group Title

what now? :o

20. AERONIK Group Title

and is it log to the base 10 or log to the base e ?

21. zepdrix Group Title

For this problem, we have to assume that they are ALL the same base. Otherwise it won't work out the same. If they're a different base, let's say A, then we exponentiate, writing each side with a base A (regardless of what A might be) and it will work out the same! :D

22. zepdrix Group Title

Different than 10 i mean*

23. AERONIK Group Title

oh ok. sorry ..

24. aceace Group Title

10 logx ∗10 logy =10 log(x+y) Recognizing that log base 10, and the exponentiation base 10 are inverse operations of one another, they essentially "cancel out". HOW DID YOU DO THIS STEP... CAN YOU SHOW ME? PLEASE

25. AERONIK Group Title

by defination if y=log x to the base a, then x is nothing but a^y, just use this and you can prove the identity.

26. zepdrix Group Title

$\large \arcsin( \sin x)=x$$\huge e^{\ln x}=x$ Yah this is true of any function and it's inverse :D Remember it in trig with the inverse functions?

27. aceace Group Title

no ...can you do a proof for it please?

28. zepdrix Group Title

|dw:1353225574033:dw| Hmmm this might be a little confusing.. I drew a lot of arrows :| lemme know if it makes some sense.

29. aceace Group Title

i get it ...thanks so much